Nonuniversality and finite dissipation in decaying magnetohydrodynamic turbulence

A model equation for the Reynolds number dependence of the dimensionless dissipation rate in freely decaying homogeneous magnetohydrodynamic turbulence in the absence of a mean magnetic field is derived from the real-space energy balance equation, leading to Cμ=Cμ,+C/R-+O(1/R-2), where R- is a generalized Reynolds number. The constant Cμ, describes the total energy transfer flux. This flux depends on magnetic and cross helicities, because these affect the nonlinear transfer of energy, suggesting that the value of Cμ is not universal. Direct numerical simulations were conducted on up to 20483 grid points, showing good agreement between data and the model. The model suggests that the magnitude of cosmological-scale magnetic fields is controlled by the values of the vector field correlations. The ideas introduced here can be used to derive similar model equations for other turbulent systems.